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YGO 2024, 8 клас, Задача 2.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл трикутника 𝐴𝐵𝐶. Точки 𝑃 та 𝑄 такі, що 𝐴𝐼𝑂𝑃 та 𝐵𝐼𝑂𝑄 — рівнобічні трапеції (𝐴𝐼||𝑂𝑃, 𝐵𝐼||𝑂𝑄). Доведіть, що 𝐶𝑃 = 𝐶𝑄.

Володимир Брайман



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YGO 2024, 8 клас, Задача 2.

Нехай 𝐼 та 𝑂 — центри вписаного та описаного кіл трикутника 𝐴𝐵𝐶. Точки 𝑃 та 𝑄 такі, що 𝐴𝐼𝑂𝑃 та 𝐵𝐼𝑂𝑄 — рівнобічні трапеції (𝐴𝐼||𝑂𝑃, 𝐵𝐼||𝑂𝑄). Доведіть, що 𝐶𝑃 = 𝐶𝑄.

Володимир Брайман

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In 2014, Pavel Durov fled the country after allies of the Kremlin took control of the social networking site most know just as VK. Russia's intelligence agency had asked Durov to turn over the data of anti-Kremlin protesters. Durov refused to do so. Now safely in France with his spouse and three of his children, Kliuchnikov scrolls through Telegram to learn about the devastation happening in his home country. Right now the digital security needs of Russians and Ukrainians are very different, and they lead to very different caveats about how to mitigate the risks associated with using Telegram. For Ukrainians in Ukraine, whose physical safety is at risk because they are in a war zone, digital security is probably not their highest priority. They may value access to news and communication with their loved ones over making sure that all of their communications are encrypted in such a manner that they are indecipherable to Telegram, its employees, or governments with court orders. Oh no. There’s a certain degree of myth-making around what exactly went on, so take everything that follows lightly. Telegram was originally launched as a side project by the Durov brothers, with Nikolai handling the coding and Pavel as CEO, while both were at VK. It is unclear who runs the account, although Russia's official Ministry of Foreign Affairs Twitter account promoted the Telegram channel on Saturday and claimed it was operated by "a group of experts & journalists."
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